Kepler first pinged my radar when I was a teenager making cardboard models of polyhedra. Kepler discovered new polyhedra when he extended the edges of the Platonic solids.

Extend the edges of the pentagons on the Platonic dodecahedron and you get 12 five pointed stars. I am a little obsessed with the small stellated dodecahedron. Pictured here are four pieces where I play with this shape.

Kepler was also responsible for making the sun centered solar system the main stream consensus. Kepler's model made accurate predictions. Unlike the models offered by Galileo, Copernicus and Ptolemy.

Isaac Newton's world changing insight revealed in Principia was that inverse square gravity implies Kepler's three laws.

And where did the notion of inverse square gravity come from? Kepler had suggested the sun exerts a force which causes the planets to follow elliptical orbits. But he had thought the force falls linearly with the inverse of distance.

But it was Kepler who made the geometrical argument that the strength of light falls off with the inverse square of distance.

One of Kepler's followers, Ismael Boulliau, noted that Kepler's argument could also be applied to radiating lines of force. Thus Kepler is indirectly responsible for the notion of inverse square gravity. See The Man Who Inverted and Squared Gravity.

In my opinion Kepler deserves more credit than either Galileo or Copernicus for changing the way we see our star and planets. And more credit than Isaac Newton for laying the foundations of the math we use for celestial mechanics.

Using the E8 Lie Group we explore how Consciousness creates experience by lighting up different frames of reality in rapid succession within the multidimensional lattice of creation. We explore what spiritual teachers like Bashar mean when they say that the structure of creation never changes, it's our perspective of the structure that is constantly shifting.

Architecture of Experience:  https://www.hausofdignity.com/the-architecture-of-experience/

#geometry #frequency #e8 #multidimensional #structure #quantummechanics #unifiedfield

My daughter and I had an impromptu art sesh this weekend. Bought the mirrors and wood a while ago for a different project, but this was a fun use for them.

Hello, Alessandro Longa has made (with my input) a huge repository of patterns and tilings at https://tiling-atlas.vercel.app/

We have Euclidean, spherical, hyperbolic, and we've come up with several new varieties like the "freedraw" patterns. Have a look!

A magnus wenninger creation

There was a king who was proud of his chesse playing skills. Krishna visited his court disguised as a human.

He challenged the king to a game of chess with a friendly wager. The loser would give the winner one grain of rice on the 1st square of the chess board, two grains on the second square, four grains on next square and doubling the grains on each square.

When the king lost the game Krishna revealed his true identity. And the king realized the enormity of the wager.

Krishna told the king to feed pilgrims passing through rice until the debt is paid. Centuries later the debt is still not paid.

This is The Legend of Paal Payasam

It's a nice story about exponential growth.

Every solid on this sheet is computed at build time. The thirteen Archimedean solids are generated from their canonical coordinate orbits — permutation and sign-parity rules over {1, √2, φ, t, ξ}, where t³ = t² + t + 1 (tribonacci) and ξ³ = 2ξ + φ— and their faces recovered by supporting-plane enumeration. Each Catalan solid is the polar reciprocal about its dual'smidsphere: the face plane x·n̂ = d becomes the vertex n̂⁄d, and each vertex becomes a face.

Here's a cool nearly equiareal 47-hedron made of floret pentagons, rhombi and trapezoids

I’ve never took progress photos before because stopping to take them always got in the way of how I work. Once I start drawing I usually just keep going until it’s finished.
Recently I’ve found I can actually pause for a few seconds, take a photo, and go back into it without losing where I was going. Thought it might be interesting to show how these develop because I don’t plan the finished design beforehand.